Blind process and receiver to determine space-time parameters of a propagation channel

ABSTRACT

Blind or partially blind process to determine characteristic space-time parameters of a propagation channel in a system comprising at least one reception sensor receiving a signal y(t). It comprises at least one step in which the specular type structure of the channel is used and a step for the joint determination of parameters such as antenna vectors (a) and/or time vectors (τ) starting from second order statistics of the received signals. 
     Application for monitoring the spectrum of a propagation channel for positioning purposes starting from one or several HF stations or for standard communication links with equalization or positioning or spatial filtering.

FIELD OF THE INVENTION

This invention relates to a process and a receiver for blindidentification of characteristic parameters of a propagation channel,particularly from second order statistics of the signal received by asensor.

For example, the identified parameters are the delay and attenuation ofchannel paths.

The invention is particularly applicable in the field of mobileradiocommunications or ionospheric HF links.

BACKGROUND

Specular Channel

HF mobile or ionospheric radiocommunications are affected by themultiple path phenomenon. In urban areas, the transmitted signal isreflected and diffracted on fixed or moving obstacles present in theenvironment. For HF transmissions, the reflections are made on differentlayers of the ionosphere. In the case of propagation channels that canbe qualified as specular, in other words the transmission takes placealong a limited number of discrete or temporary paths characterized by adelay and a complex attenuation. Assuming an observation time compatiblewith the stationarity duration of the channel, multi-sensor receptionand specular propagation, the expression for the multi-sensor channelis:

$\begin{matrix}{{c(t)} = {\sum\limits_{k = 1}^{d}\;{a_{k}{\delta\left( {t - \tau_{k}} \right)}}}} & (1)\end{matrix}$where k is the index of a path, a_(k) is the vector for which thecomponents are complex attenuations of the path k for the differentchannels, τ_(k) is the delay associated with the kth path and d is thenumber of paths in a channel.

Furthermore, if each path k is incident on the network following areduced spatial diffusion cone, the expression (1) is in the followingform

$\begin{matrix}{{c(t)} = {\sum\limits_{k = 1}^{d}\;{\beta_{k}{a\left( \theta_{k} \right)}{\delta\left( {t - \tau_{k}} \right)}}}} & (2)\end{matrix}$where a(θ_(k)) is the input vector for an angle associated with the kthpath and β_(k) is the complex attenuation of the path.

In the first case (Eq. 1), the channel is not defined by parametersrelated to the direction from which the paths arrive, each propagationpath is defined by parameters consisting of an arrival time τ and an<<antenna vector>> a. Thus, the calibration is no longer necessary andalgorithms are no longer limited by spatial dispersion or coherentpaths.

In the second case (Eq. 2), paths are defined by parameters consistingof their directions of arrival, which assumes that the type of theantenna is known and therefore generally involves setting up acalibration to estimate the values of θ_(k).

Blind Identification

In active or driven systems, the channel parameters are calculatedduring a learning phase in which the transmitter transmits a sequenceknown to the receiver.

If the propagation channel fluctuates in time, particularly due tomovements of mobile stations or ionospheric layers, the sequence must besent periodically in order to update the value of the parameters.

If this type of system is efficient, the regular transmission of alearning sequence can cause a significant reduction in the effectivethroughput.

For example, in the STANAG 4285 standard for cooperative ionospheric HFtransmissions, half of the transmitted symbols are learning symbols.

Prior art also includes different blind methods and systems, in whichparameters are estimated starting from statistics of the receivedsignal, without any advance knowledge of the learning sequence.

Second Order Techniques

For example, the proposed techniques simply use second order statistics(space-time covariance matrix) of the received signal. Second orderalgorithms have better convergence properties than higher orderalgorithms, i.e. the variance of second order estimators for a givennumber of symbols, is usually less than the variance of estimators withhigher orders. Furthermore, they have fewer local optimisation problemsthan techniques with higher orders.

Various methods and algorithms have been developed, such as thosedescribed in document entitled “Multichannel Blind Identification : fromsubspace to maximum likelihood methods” by L. Tong and S. Perreau;Proceedings of the IEEE, 86(10): 1951-1967, October 1998. One of thedisadvantages of these algorithms is that the length of the globaltransmission channel has to be known, and most of them are intolerant toan error in the estimate of this length. When the bandwidth of thetransmission is limited, the channel length is only definedapproximately and these algorithms can no longer be used.

State of the Art for Blind Parametric Identification

Most work on blind identification of characteristic propagationparameters uses decoupled algorithms, i.e. algorithms that independentlyestimate arrival times and antenna vectors or arrival directions. Theseinclude direction finding algorithms to estimate directions of arrival,and coherent source separation algorithms to estimate antenna vectors. Alot of work has also be done on estimating arrival times.

Joint estimating methods can improve the precision and resolution ofestimators, such that parameters can be estimated even when delays (orangles) are very similar.

The main work done on blind joint estimating of parameters (θ,τ) isdescribed in the following references:

-   -   “Identification spatio-temporelle de canaux de propagation à        trajets multiples” (“Space-time identification of multipath        propagation channels) by J. Gouffraud, PhD thesis, Ecole Normale        Supérieure de Cachan, 1997, and    -   “Improved blind channel identification using a parametric        approach” by M. C. Vanderveen and A. Paulraj, IEEE        Communications Letters, pages 226-228, August 1998.

The idea is that criteria used to make a blind estimate of the pulseresponse may be directly minimized as a function of the angles anddelays, using subspace type criteria like those described in the“Subspace methods for the blind identification of multichannel FIRfilters” paper by E. Moulines, P. Duhamel, J-F. Cardoso and S.Mayrargue, IEEE Trans. on signal Processing, 43(2): 516-525, February1995. These algorithms require that the transmission/reception filter isknown in advance and that the antenna is calibrated.

Furthermore, an example of a method of making a joint blind estimate ofparameters (a,τ) is described in the “Methods for blind equalization andresolution of overlapping echoes of unknown shape” paper by A.Swindlehurst and J. Gunther, IEEE Trans. on Signal Processing, 47(5):1245-1254, May 1999. The authors work in the frequency range and proposean iterative IQML type algorithm to give an approximate solution with amaximum probability and an explicit initialisation algorithm based onthe ESPRIT algorithm. These algorithms do not require advance knowledgeof the transmission filter, but do have the disadvantage that a Fouriertransformation is necessary before processing.

SUMMARY OF THE INVENTION

The invention relates to a blind or partially blind process that candetermine at least the characteristic space-time parameters of apropagation channel in a system comprising at least one sensor forreception of signals y(t), characterized in that it comprises at leastone step in which the specular type structure of the channel is takeninto account and a step for the joint determination of space-timeparameters such as antenna vectors (a) and/or time vectors (τ) startingfrom second order statistics of the signals received on one or severalsensors.

According to one embodiment, it comprises a step in which the receivedsignal y(t) is oversampled, for example with a sampling period equal toT/p, where T is the symbol period.

According to another embodiment, the process comprises a reception stepon at least two sensors and an oversampling step.

For example, the process according to the invention may be applied forstandard links for equalization, positioning and spatial filteringpurposes, or for monitoring the spectrum of a propagation channel forpositioning purposes starting from one or several HF stations.

In particular, the invention has the following advantages:

-   -   there is no need to transmit a learning sequence that may reduce        the effective transmission throughput, or to know the length of        the global transmission channel,    -   it is tolerant to an overestimate of the order of the        transmission channel.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantages and characteristics of the invention will become clearafter reading the following description with reference to the singleFIGURE given for illustrative purposes and in no way limitative, andthat shows the schematic for a radio-communication receiver according tothe invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

We will mention a few remainders, assumptions and definitions beforegoing on to describe the steps in the process according to theinvention.

Assumptions and Model

The Single Sensor Signal Model

The transmitted signal is in the form

$\begin{matrix}{{x(t)} = {\sum\limits_{l \in Z}{{g\left( {t - {IT}} \right)}{s(I)}}}} & (3)\end{matrix}$where g(t) is the transmission/reception filter and values in {s(I)} areinformation symbols that were sent at the symbol period T.

The system assumes that the carrier frequency and the symbol period areestimated in advance. The signal received in base band is written

$\begin{matrix}{{y(t)} = {{\sum\limits_{l \in Z}{{h\left( {t - {IT}} \right)}{s(I)}}} + {w(t)}}} & (4)\end{matrix}$where the values of {s(I)} are information symbols that were sent at thesymbol period T, h(t) is the pulse response of the transmission channel,and w(t) is an additive noise. The received signal sampled at the symbolperiod follows the discrete model:

$\begin{matrix}{{y(k)} = {{{y({kT})}{\sum\limits_{l \in Z}{{h\left( {k - I} \right)}{s(I)}}}} + {w(k)}}} & (5)\end{matrix}$where h(I)=h(IT) (assuming that the sampling phase is equal to 0).The Multichannel System

FIG. 1 represents a multichannel reception system comprising a number qof reception sensors and a means of oversampling the signal s(k)corresponding to path index k.

Obviously, without going outside the framework of the invention, theprocess can also apply to receivers comprising several sensors withoutany means of oversampling, or comprising a single sensor and a means ofoversampling the received signal.

In the example embodiment given below, the device considered is amultichannel system combining spatial diversity and time diversity, i.ethe signal is received on a network of q sensors Ci each having aresponse h_((i))(t) and it is then oversampled with respect to thesymbol period T, at the rate T/p as shown in FIG. 1. Oversampling isdone using an appropriate device. The global pulse response of thetransmission channel and the multi-sensor observations vector aredefined by the following q×1 column vectors:h(t)=[h ₍₁₎(t), . . . , h _((q))(t)]^(T)  (6)y(t)=[y ₍₁₎(t), . . . , y _((q))(t)]^(T)  (7)

The subscript indicates the sensor number and the superscript Trepresents the transpose of a matrix. Bold characters indicate a spatialdimension. The samples obtained by sampling at rate T/p are vectorizedby collecting signals sampled in the same sampling phase within a symbolperiod. More precisely, a path is associated with each of the pdifferent sampling phases at the symbol rate, thus creating a multipathchannel with p outputs on each sensor. This gives a multipath channelwith p.q outputs. The global pulse response of the transmission channeland the multipath observations vector are defined by the followingcolumn vectors p.q×1:h (k)=[h ⁽¹⁾(kT) . . . h ^((p))(kT)]^(T)  (8)y (k)=[y ⁽¹⁾(kT) . . . y ^((p))(kT)]^(T)  (9)The superscript indicates the sampling phase,h ^((i))(kT)=h(kT+(i−1)T/p), y ^((i))(kT)=y(kT+(i−1)T/p).Assumptions

The process according to the invention is based on a number ofassumptions, and particularly the following.

Symbols Source

H 1—For example, process {s(k)} is a complex white noise that may alsobe circular at the second order of unit variance,E[s(k)]=0, E[s(k)s(j)^(H)]=δ(k−j), E[s(k)s(j)]=0  (10)NoiseH 2—Noise w(k) is a Gaussian, circular, white process stationary inspace and time with variance σ²,E[w (k) w (k)^(H)]=σ² Ipq  (11)where Ipq is the identity matrixTransmission/Reception FilterH 3—The transmission/reception filter g(t) has a finite support, g(t)=0for t ∉[0, LgT[ where Lg corresponds to the filter length and T to thesampling period.H 4—The transmission/reception filter g(t)⇄G(f) is approximately asfollows for a limited band, with band B_(g)G(f)≈0∀f∉[−B _(g) ,B _(g)]  (12)and G(f) does not cancel out within a given band β,G(f)≠0∀f∈[−B _(g) ,B _(g)]  (13)Propagation ChannelH 5—The signal is a narrow band for the sensor network, i.e. it isassumed that the propagation time for the signal to pass from one sensorto the next is very much less than the inverse of the signal band.H 6—The channel is constant over an observation interval. The Dopplershift and carrier residues are assumed to be negligible.H 7—The time difference between the first and last path is finite, andit has an upper limit: Δτ_(max).where d is the number of paths and τ_(k) is the delay and a_(k) is thevector of q×1 dimension antennas associated with the kth path, thechannel response being expressed as follows.

$\begin{matrix}{{h(t)} = {\sum\limits_{k = 1}^{d}\;{a_{k}{g\left( {t - \tau_{k}} \right)}}}} & (14)\end{matrix}$By sampling at T/p,

$\begin{matrix}{{h_{\frac{T}{p}}(z)} = {{\sum\limits_{k = {- \infty}}^{\propto}\;{{h\left( {{kT}/p} \right)}z^{- k}}} = {\sum\limits_{k = 1}^{d}\;{a_{k}{g_{\frac{T}{p}}\left( {\tau_{k};z} \right)}}}}} & (15)\end{matrix}$where

$\begin{matrix}{{g_{\frac{T}{p}}\left( {\tau;z} \right)}\underset{\_}{\underset{\_}{\Delta}}{\sum\limits_{n}{{g\left( {{n\frac{T}{p}} - \tau} \right)}z^{- n}}}} & (16)\end{matrix}$is the transform into z of the transmission/reception filter shifted byτ and sampled at T/p.Furthermore, h(z) is the response in z to the symbol rate of thecombined system,

$\begin{matrix}{{\underset{\_}{h}(z)} = {\sum\limits_{k = {- \infty}}^{\infty}\;{{\underset{\_}{h}({kT})}z^{- k}}}} & (17)\end{matrix}$The received signal follows the equivalent single source multi-outputdiscrete model:y (k)=[h(z)]s(k)+ w (k)  (18)it is interesting to note that

$\begin{matrix}{{h_{\frac{T}{p}}(z)} = {\sum\limits_{i = 1}^{p}\;{{h^{(i)}\left( z^{p} \right)}z^{- i}}}} & (19)\end{matrix}$where h^((i))(z)=Σ_(k=−∞) ^(∞) h^((i))(k)Z^(−k) are the multi-phasecomponents of the oversampled channel.

According to assumptions H3 and H7, the pulse response of the globalmulti-sensor transmission channel has a finite length.

Therefore, the degree of the discrete responses h(z) and h_(T/p)(z) isfinite. We note L=deg(h) i.e. the degree of at least one of the paths isequal to L, the degrees of the others may be lower,h(z)= h (0)+ h (1)z ⁻¹ + . . . +h (L)z ^(−L)Similarly, we denote L_(T/p)=deg(h_(T/p)). We have pL≦L_(T/p≦)p(L+1)−1.In order to simplify the presentation, we assume thatL _(T/p)+1=p(L+1).

Furthermore, second order algorithms are based on the followingdiversity condition for the global transmission channel:

H 8 The polynomial vector h(z) is irreducible, i.e. these components donot have any common roots.

Some Notations and Tools

If {b⁽¹⁾(z), . . . , b^((r))(z)} are r scalar polynomials,

b(z)=[b⁽¹⁾(z), . . . , b^((r))(z)]^(T) is a polynomial vector (a vectorfor which the coordinates are polynomials) with dimension r. The maximumdegree of the polynomials is called the order or the degree of thevector deg(b(z))

{b⁽¹⁾(z), . . . , b^((r))(z)}. If L_(b) is the degree of b(z), then

$\begin{matrix}{{b(z)} = {\sum\limits_{k = 0}^{L\; b}{{b(k)}z^{- k}}}} & (20)\end{matrix}$where b(k)=[b⁽¹⁾(k) , . . . , b^((r))(k)]^(T). The vector associatedwith b(z), i.e. containing all its coefficients, is denoted by an arrow,{right arrow over (b)}=[b(0)^(T) . . . b(L _(b))^(T)]^(T)  (21)

with dimension r(L_(b)+1)×1. Therefore, in particular {tilde over (h)}

corresponds to the dimension vector

q.p(L+1)×1 associated with h(z) and h_(T/p)(z)

i.e. containing all their coefficients,{right arrow over (h)}=[h (0)^(T) . . . h (L)^(T)]^(T)

$\begin{matrix}{\overset{\rightarrow}{h} = \left\lbrack {{\underset{\_}{h}(0)}^{T}\ldots\mspace{14mu}{\underset{\_}{h}(L)}^{T}} \right\rbrack^{T}} & (22) \\{\mspace{14mu}{= \left\lbrack {{h_{\frac{T}{p}}(0)}^{T}\ldots\mspace{14mu}{h_{\frac{T}{p}}\left( L_{\frac{T}{p}} \right)}^{T}} \right\rbrack^{T}}} & (23)\end{matrix}$Furthermore, let K be an integer defining the number of multidimensionalobservations, _(k)(b) is the Sylvester matrix (i.e. Toeplitz per block)with dimension r(K+1)×(K+L_(b)+1) associated with the polynomial b(z),and defined by

$\begin{matrix}{{\tau_{k}(b)} = \begin{bmatrix}{b(0)} & \ldots & {b\left( L_{b} \right)} & 0 & \ldots & 0 \\0 & {b(0)} & \; & {b\left( L_{b} \right)} & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & \; & ⋰ & 0 \\0 & \ldots & 0 & {b(0)} & \ldots & {b\left( L_{b} \right)}\end{bmatrix}} & (24)\end{matrix}$Finally, let B(z) be a polynomial matrix with dimension r×D and degreeL_(b),B(z)=[b ₁(z), . . . , b _(D)(z)]where b_(i)(z) is a polynomial vector with dimension r. We will useB=[{right arrow over (b)} ₁ , . . . , {right arrow over (b)} _(D)]to denote the associated matrix with dimensions r(L_(b)+1)×D, andD_(K)(B) to denote the Sylvester block matrix with dimensionsr(K+1)×(K+L_(b)+1)D defined byD _(k)(B)=[T _(k)(b ₁), . . . , T _(k)(b _(D))]  (25)λ_(min)(A) denotes the smallest eigenvalue of matrix A and vp_(min)(A)is the eigenvector associated with λ_(min)(A).Process According to the Invention

The process according to the invention is based particularly on takingaccount of the specular type channel structure to determine the specificparameters of a signal propagation or transmission channel, particularlyin a communication system like that shown in FIG. 1. For example, theparameters determined jointly may be the time vector (τ) of delayvectors (τ_(k)), and the antenna vector (a) of vectors (a_(k)).

A first alternative embodiment of the process or the “a priori process”is particularly suitable when the transmission/reception filter isknown.

A second alternative embodiment of the process or “no a priori process”is more suitable for the case in which the characteristics of thetransmission/reception filter are not known.

A Priori Process

The process assumes that the transmission filter g(t) is known. Thevarious steps in the a priori process or algorithm according to theinvention are based on the fact that equation (15) is written in“vectorial” form as follows:{right arrow over (h)}=G _(L,d)(τ)a  (26){right arrow over (h)} is the vector with dimension q.p.(L+1) containingall coefficients of the response h_(T/p)(z), a is the vector withdimension q.d containing all antenna vectors a=[a_(l) ^(T) . . . a_(d)^(T)]^(T)and G_(L,d)(τ) is a matrix with dimension q.p(L+1)×q.d containingdelayed versions sampled at T/p of the transmission filter:

$\begin{matrix}{{G_{L,d}(\tau)} = {\begin{pmatrix}{g\left( {0 - \tau_{l}} \right)} & \ldots & {g\left( {0 - \tau_{d}} \right)} \\{g\left( {\frac{T}{p} - \tau_{l}} \right)} & \ldots & {g\left( {\frac{T}{p} - \tau_{d}} \right)} \\\vdots & \; & \vdots \\{{{g\left( {L + 1} \right)}T} - \frac{T}{p} - \tau_{l}} & \ldots & {{{g\left( {L + 1} \right)}T} - \frac{T}{p} - \tau_{d}}\end{pmatrix} \otimes I_{q}}} & (27)\end{matrix}$I_(q) is the identity matrix with dimension q. We will use τ to denotethe vector with dimension d containing all delays τ=[τ_(l), . . . τ_(d)]

For example, the different steps in the process could be as follows:

1. Choose the length of the global propagation channel taking account oftransmission and reception, {circumflex over (L)}≧L_(g)+Δτ_(max) and thevalue of the number of observations K≧{circumflex over (L)} whereΔτ_(max) is the largest possible value of the relative delay between twopaths.2. Calculate the sub-space criterion matrixQ_({circumflex over (L)})({circumflex over (R)}), for example asfollows:

-   -   Calculate the empirical estimate of the covariance matrix:

$\begin{matrix}{\hat{R} = {\frac{1}{N - K}{\sum\limits_{k = 0}^{N - K}{{\overset{\rightarrow}{y\;}}_{K}(k){{\overset{\rightarrow}{y}}_{K}(k)}^{H}}}}} & (28)\end{matrix}$where{right arrow over (y)} _(K)(k)=[y(0)^(T) y(T/p)^(T) . . .y(KT−T/p)^(T)]^(T)  (29)=] y (0)^(T) . . . y (K)^(T)]_(pg(K−1)) ^(T)  (30)and let N-K be the number of independent observations.

-   -   Build the matrix Ĝ_({circumflex over (L)}) for example using the        eigenvectors associated with the pq(K+1)−(K+{circumflex over        (L)}+1) smallest eigenvalues of {circumflex over (R)}.        Ĝ_({circumflex over (L)}) can also be obtained from the        breakdown of the data matrix Y=⁶⁶ [{right arrow over (y)}(K) . .        . {right arrow over (y)}(N)].) into eigenelements. Then form the        projection matrix {circumflex over        (Π)}_({circumflex over (L)})=Ĝ_({circumflex over (L)})Ĝ_({circumflex over (L)})        ^(H)    -   Form the sub-space criterion matrix        Q_({circumflex over (L)})({circumflex over        (R)})=D_({circumflex over (L)})({circumflex over        (Π)}_({circumflex over (L)}))D_({circumflex over (L)})({circumflex        over (Π)}_({circumflex over (L)}))^(H)        3. Estimate the number of paths, for example {circumflex over        (d)}, by using the method described in the “Detection of signals        by information theory criteria” reference by M. Wax and T.        Kailath, IEEE Trans.on Acoust. and Sig. Proc., 33(2): 387-392,        April 1985.        4. Estimate the delays

$\begin{matrix}{{\hat{\tau} = {\arg\;{\min\limits_{\tau}{J_{\hat{L},\hat{d}}(\tau)}}}}{where}} & \; \\{{J_{\hat{L},\hat{d}}(\tau)} = \frac{\lambda_{\min}\left( {{G_{\hat{L},\hat{d}}(\tau)}^{H}{Q_{\hat{L}}\left( \hat{R} \right)}{G_{\hat{L},\hat{d}}(\tau)}} \right)}{\lambda_{\min}\left( {{G_{\hat{L},\hat{d}}(\tau)}^{H}{G_{\hat{L},\hat{d}}(\tau)}} \right)}} & (31)\end{matrix}$

This is done by applying the iterative process described below:

-   -   Let d=1. Obtain an estimate {circumflex over (τ)}₁ of τ₀₁ by        minimizing {hacek over        (J)}_({circumflex over (L)},{circumflex over (d)})(τ₁)    -   Let d=2. Obtain and estimate {circumflex over (τ)}₂ of τ₀₂ by        minimizing {hacek over        (J)}_({circumflex over (L)},{circumflex over (d)})([τ₁,τ₂])        as a function of τ₂ and keeping τ₁ equal to the estimate        {circumflex over (τ)}₁ obtained in the first step. Then, obtain        a new estimate of [τ₀₁, τ₀₂] using a multidimensional        minimization of {hacek over        (J)}_({circumflex over (L)},{circumflex over (d)})([τ₁,τ₂]) and        using the values [{circumflex over (τ)}₁, {circumflex over        (τ)}₂] that were obtained above as initial values.    -   Iterate this process until d={circumflex over (d)}, for all        possible paths in order to obtain the delay vector.        5. Estimate the value of the antenna vector by        â=vp _(min)(G _({circumflex over (L)}),{circumflex over        (d)}(τ)^(H) Q _({circumflex over (L)})({circumflex over        (R)})G_({circumflex over (L)}),{circumflex over (d)}({circumflex        over (τ)}))        6. Create the estimate of the pulse response: {right arrow over        (ĥ)}=G_({circumflex over (L)},{circumflex over (d)})({circumflex        over (τ)})â        No A Priori Process

The second alternative of the process corresponds to a parameterestimating algorithm that is entirely or mostly blind. As in the firstalternative embodiment, the associated algorithm takes account of thespecular nature of the propagation channel in order to determine itsparameters, and particularly the antenna vector and the characteristicstime vector. Unlike the first variant, it does not require advancedknowledge of the transmission filter. It simply assumes that thetransmission filter has a limited band and that its band is knownapproximately.

For example, the various steps in the process or algorithm are asfollows:

1. Estimate {circumflex over (L)}g, the length of the transmissionfilter, and choose {circumflex over (L)}≧{circumflex over(L)}_(g)+Δτ_(max) and K≧{circumflex over (L)}

2. Apply the sub-space method described in item 2 of the a prioriprocess:

-   -   Estimate the covariance matrix {circumflex over (R)}, for        example using the steps described above corresponding to        equation (Eq. 28).    -   Calculate the projection matrix on the noise space {circumflex        over (Π)}_({circumflex over (L)}) starting from the eigenvectors        associated with the pq(K+1)−(K+{circumflex over (L)}+1) null        eigenvalues of the matrix {circumflex over (R)}.    -   Form the matrix Q_({circumflex over (L)})({circumflex over        (R)})=D_({circumflex over (L)})({circumflex over        (Π)}_({circumflex over (L)}))D_({circumflex over (L)})({circumflex        over (Π)}_({circumflex over (L)}))^(H)    -   Obtain {right arrow over (ĥ)} the eigenvector associated with        the smallest eigenvalue of the matrix        Q_({circumflex over (L)})({circumflex over (R)}) and form

${\hat{h}}_{\frac{T}{p}}(z)$3. Form the new parametric criterion:

-   -   Choose the value of the channel length

${R \geq {\hat{L}}_{\frac{T}{p}}} = {{p\left( {\hat{L} + 1} \right)} - 1}$

-   -   and form the matrix

$\tau_{R}\left( {\hat{h}}_{\frac{T}{p}} \right)$

-   -   Calculate the matrix

${\hat{\Omega}}_{{\hat{L}}_{\frac{T}{p}}}$containing eigenvectors associated with the

${q\left( {R + 1} \right)} - {\left( {R + {\hat{L}}_{\frac{T}{p}} + 1} \right)\mspace{14mu}{smallest}\mspace{14mu}{eigenvalues}\mspace{14mu}{of}\mspace{14mu}{\tau_{R}\left( {\hat{h}}_{\frac{T}{p}} \right)}^{H}}$$\text{-}{Form}\mspace{14mu}{the}\mspace{14mu}{matrix}\mspace{11mu} D_{{\hat{L}}_{\frac{T}{p}}}\;\left( {\hat{\Omega}}_{{\hat{L}}_{\frac{T}{p}}} \right)$4. Estimate the number of paths {circumflex over (d)}, for example usingthe method referenced above for step 3 in the first alternativeembodiment.5. Determine the minimum value of the band of the transmission filter:β, usually β=1/T.6. Choose {tilde over (v)}(t), a continuous filter with band limited tothe β band. Form the filter v(t),

$\begin{matrix}\left\{ \begin{matrix}{{v(t)} = {\overset{\sim}{v}(t)}} & {0 \leq t \leq {Lv} \leq {\hat{L}g}} \\{{v(t)} = 0} & {elsewhere}\end{matrix} \right. & (32)\end{matrix}$7. Estimate the delays

$\begin{matrix}{{\hat{\tau} = {\arg\;{\min\limits_{\tau}{I_{\hat{L},\hat{d}}(\tau)}}}}{where}} & \; \\{{I_{\hat{L},\hat{d}}(\tau)} = \frac{\lambda_{\min}\left( {{V_{\hat{L},\hat{d}}(\tau)}^{H}{D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)}{D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)}^{H}{V_{\hat{L},\hat{d}}(\tau)}} \right)}{\lambda_{\min}\left( {{V_{\hat{L},\hat{d}}(\tau)}^{H}{V_{\hat{L},\hat{d}}(\tau)}} \right)}} & (33)\end{matrix}$using the iterative process proposed for the parametric subspace method.(The matrix V_({circumflex over (L)},{circumflex over (d)})(τ) isdefined in the same way as the matrixG_({circumflex over (L)},{circumflex over (d)})(τ) but from the filterv(t).)8. Estimate antenna vectors:

$\begin{matrix}{\hat{a} = {{vP}_{\min}\left( {{V_{\hat{L},\hat{d}}\left( \hat{\tau} \right)}^{H}{D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)}{D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)}^{H}{V_{\hat{L},\hat{d}}\left( \hat{\tau} \right)}} \right)}} & (34)\end{matrix}$Possible Applications

The process according to the invention is applied, for example in thedomains mentioned below for illustrative purposes and in no waylimitative.

Cellular Networks

For cellular transmissions, the transmission standard is known.Therefore, the standard transmission filter is known and it ispreferable to apply the a priori process using advance knowledge of thetransmission/reception filter. The potential applications are asfollows:

Equalization

Propagation acts as time convolution. Except for very low throughputcommunications (a few hundred bits per second), this time dispersioninduced by propagation creates interference between symbols (IES). Inorder to best recover the transmitted symbols, the dispersive effect ofthe channel must be compensated by an equalization step like thatdescribed in the book entitled “Digital Communications”, written by J.G. Proakis and published by McGraw Hill editions, 1989. If thetransmission/reception filter is known, the global response can be builtup starting from knowledge of propagation channel parameters, and anequalization step can be applied. The advantage of this approach is thatin general, by estimating propagation parameters rather than the globalresponse, the number of parameters to be estimated is smaller so that itis usually possible to reduce the variance of the estimators. Theidentification quality and equalization performances can thus beimproved significantly. Furthermore, some characteristic parameters ofthe propagation channel (arrival delays and angles) do not change verymuch from one frame to the next. Parametric modelling makes it moreefficient to monitor variations of channel parameters and furtherimproves the identification quality, for example such as described inthe “Multi-channel MLSE equalizer with parametric FIR channelidentification” reference by J. T. Chen and A. Paulraj, in VTC, Proc.,pages 710-713, 1997.

Positioning

Positioning of the transmitter is a classical problem in militaryapplications, and has recently become the subject of close attention forcivil applications in mobile communications. Positioning of mobiles in acellular network makes it possible to provide many services such aspositioning of emergency calls, management of charging, detection offraud, assistance with cellular planning, improvement in organizing the“handover” as described in “Position location using wirelesscommunications on highways of the future” reference by T. S. Rappaport,J. H. Reed and B. D. Woerner, IEEE Commun. Mag., October 1996.

Several techniques can be used for positioning. The most classical istriangularization. In this case, positioning is done using two or threeseparate receivers (base stations) each estimating the angles and/orarrival times of the transmitted signal as described in the “MobileLocalization in a GSM Network ” reference by H. El Nahas, PhD thesisENST, June 1999. This system has some disadvantages, which is whypositioning algorithms from a single station were developed. Thesepositioning techniques always require prior knowledge of propagationcharacteristics. For example, a positioning process is described in thereference entitled “Procédés de localisation spatio-temporel deradiomobiles en milieu urbain” (Space-time positioning processes forradiomobiles in urban environment) by M. Chenu-Tournier, A. Ferréol andJ-J. Monot, Technical report, TCC, 1997.

Antenna Filtering—SDMA

Knowledge of spatial characteristics of the different paths may be usedto focalise transmission in the main arrival direction and thus minimizethe effect of multiple paths on receivers (uplink beamformer design,downlink transmission design).

Spectrum Monitoring

In the context of a spectrum radio-electrical analysis, the receiver hasno prior knowledge about the transmitter. The reception system scans thespectrum, intercepts a signal transmitted by an unknown transmitter andanalyses it to extract some information from it to be able to listen tothe transmission or determine the position of the transmitter. In thiscontext, it is unlikely that the transmission filter will be known andthe no a priori process is the most suitable for estimating propagationchannel parameters (τ; a). In this case, since the transmission filteris not known, it is impossible to equalize the received signal, butknowledge of parameters (τ; a) would make it possible to use theapplications mentioned below.

Positioning

The main application is positioning. In HF, positioning with a singlestation conventionally uses an initial step of ionospheric forecasts.Knowing the angle of incidence and the electronic density profile (byionospheric forecasting), a ray plotting method using Descartes law canbe used to reconstitute the path of the wave received on the sensorsnetwork according to one of the following references:

-   -   “Comparison of the fixing accuracy of single-station location of        long range transmitters, by H. C. Höring, IEEE Proceedings,        37(3): 173-176, June 1990.    -   “Ioniospheric modelling in support of single station location of        long range transmitters by L. F. McNamara, Journal of        Atmospheric and terrestrial Physics, 50(9): 781-795, 1988.

Knowledge of arrival times can also eliminate some ambiguities due tomulti-skip.

Others

Spatial filtering is possible if antenna vectors are known. Knowledge ofdelays is a means of recombining propagation paths in phase. The use ofone or both of the two known values may be a first step in implementinga signal analysis system.

1. A blind or partially blind process to determine characteristicspace-time parameters of a propagation channel in a system comprising atleast one reception sensor, the process comprising: receiving a signaly(t) with the at least one reception sensor; determining antenna vectors(a) and time vectors (τ) starting from second order statistics of thereceived signals based on a specular structure of the propagationchannel; selecting a length of the propagation channel {circumflex over(L)} such that {circumflex over (L)}≧Lg+Δτ_(max), where Lg denotes afilter length and Δτ_(max) denotes a largest possible value of arelative delay between two paths, and a value of a number ofobservations K satisfies K≧{circumflex over (L)}; determining asub-space criterion matrix Q_({circumflex over (L)})({circumflex over(R)}), where {circumflex over (R)} denotes a covariance matrix;estimating a number of paths {circumflex over (d)}; estimating delays{circumflex over (τ)}, where${\hat{\tau} = {{ar}\underset{\tau}{{g\mspace{11mu}\min}\;}{J_{\hat{L}.\hat{d}}(\tau)}}},$ where${{J_{\hat{L}.\hat{d}}(\tau)} = \frac{\lambda_{\min}\left( {{G_{\hat{L}.\hat{d}}(\tau)}^{H}{Q_{\hat{L}}(R)}{G_{\hat{L}.\hat{d}}(\tau)}} \right)}{\lambda_{\min}\left( {{G_{\hat{L}.\hat{d}}(\tau)}^{H}{G_{\hat{L}.\hat{d}}(\tau)}} \right)}},$ λ_(min) denotes a smallest eigenvalue of a matrix, and(G_({circumflex over (L)},{circumflex over (d)})(τ)) denotes a matrixcontaining delayed sampled versions of the received signal; estimating avalue of an antenna vector â byâ=vp_(min)(G_({circumflex over (L)},{circumflex over (d)})(τ)^(H)Q_({circumflex over (L)})({circumflexover (R)})G_({circumflex over (L)},{circumflex over (d)})(τ)), wherevP_(min) denotes an eigenvector associated with λ_(min); and forming anestimate of a pulse response ĥ such thatĥ=G_({circumflex over (L)},{circumflex over (d)})(τ)â.
 2. The processaccording to claim 1, further comprising: oversampling the receivedsignal.
 3. The process according to claim 1, wherein the receivingincludes receiving the signal on at least two sensors, and the methodfurther comprises: oversampling the received signal.
 4. The processaccording to claim 3, wherein a sampling period corresponds to T/p,where T denotes a symbol period and p denotes a number of outputs oneach sensor.
 5. A blind or partially blind process to determinecharacteristic space-time parameters of a propagation channel in asystem comprising at least one reception sensor, the process comprising:receiving a signal y(t) with the at least one reception sensor;determining antenna vectors (a) and time vectors (τ) starting fromsecond order statistics of the received signals based on a specularstructure of the propagation channel; estimating {circumflex over (L)}g,which denotes a length of a transmission filter and choosing {circumflexover (L)} such that {circumflex over (L)}≧{circumflex over(L)}g+Δτ_(max) and K≧{circumflex over (L)}, where {circumflex over (L)}denotes a length of the propagation channel, Δτ_(max) denotes a largestpossible value of a relative delay between two paths, and K denotes avalue of a number of observations; determining a sub-space criterionQ_({circumflex over (L)})({circumflex over (R)}), said determiningincluding, estimating a covariance matrix {circumflex over (R)},calculating a projection matrix onto noise space {circumflex over(Π)}_({circumflex over (L)}) using eigenvectors associated withpq(K+1)−(K+{circumflex over (L)}+1) null eigenvalues of the covariancematrix {circumflex over (R)}, where q denotes a number of receptionsensors and p denotes a number of outputs on each sensor, and formingmatrix Q_({circumflex over (L)})({circumflex over(R)})=D_({circumflex over (L)})({circumflex over(Π)}_({circumflex over (L)}))D_({circumflex over (L)})({circumflex over(Π)}_({circumflex over (L)}))^(H); obtaining an {right arrow over (h)}eigenvector associated with a smallest eigenvalue of the matrixQ_({circumflex over (L)})({circumflex over (R)}) and forming${\hat{h}}_{\frac{T}{p}}(z)$  which represents a discrete response andT/p denotes a sampling rate, where T denotes a symbol period; choosing avalue of the propagation channel length such that${R \geq {\hat{L}}_{\frac{T}{P}}} = {{p\left( {\hat{L} + 1} \right)} - 1}$forming a matrix τ_(R)(ĥ_(T/p)); calculating a matrix${\hat{\Omega}}_{\hat{L}\frac{T}{p}}$  containing eigenvectorsassociated with${q\left( {R + 1} \right)} - \left( {R + {\hat{L}}_{\frac{T}{p}} + 1} \right)$ smallest eigenvalues of τ_(R); forming matrix${D_{{\hat{L}}_{\frac{T}{p}}}\left( {\hat{\Omega}}_{{\hat{L}}_{\frac{T}{p}}} \right)};$estimating a number of paths {circumflex over (d)}; choosing {tilde over(v)}(t) to have a continuous filter with a limited band B and formingfilter v(t), $\quad\left\{ {\begin{matrix}{{v(t)} = {\overset{\sim}{v}(t)}} & {0 \leq t \leq {Lv} \leq {\hat{L}g}} \\{{v(t)} = 0} & {elsewhere}\end{matrix};} \right.$ estimating delays {circumflex over (τ)} suchthat${\hat{\tau} = {\arg{\;\;}{\min\limits_{\tau}\;{I_{\hat{L},\hat{d}}(\tau)}}}},$ where$\;{{I_{\hat{L},\hat{d}}(\tau)} = {\frac{\lambda_{\min}\left( {\left( {V_{\hat{L},\hat{d}}(\tau)} \right)^{H}{D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)}\left( {D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)} \right)^{H}{V_{\hat{L},\hat{d}}(\tau)}} \right)}{\lambda_{\min}\left( {\left( {V_{\hat{L},\hat{d}}(\tau)} \right)^{H}{V_{\hat{L},\hat{d}}(\tau)}} \right)}.}}$ λ_(min) denotes the smallest eigenvalue of a matrix, andV_({circumflex over (L)},{circumflex over (d)})(τ) denotes a matrixcontaining delayed sample versions of the received signal; andestimating a value of an antenna vector â by${\hat{a} = {{vP}_{\min}\left( {\left( {V_{\hat{L},\hat{d}}\left( \hat{\tau} \right)} \right)^{H}{D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)}\left( {D_{\hat{L}\frac{T}{p}}\left( {\hat{\Omega}}_{\hat{L}\frac{T}{p}} \right)} \right)^{H}V_{\hat{L},\hat{d}}\left( \hat{\tau} \right)} \right)}},$ where vP_(min) denotes an eigenvector associated with λ_(min).
 6. Theprocess according to claims 1 or 5, further comprising: monitoring aspectrum of the propagation channel for positioning purposes from one orseveral HF stations.
 7. The process according to claims 1 or 5, furthercomprising: equalizing, positioning, or spatial filtering standardcommunication links.
 8. The process according to claim 5, furthercomprising: oversampling the received signal.
 9. The process accordingto claim 5, wherein the receiving includes receiving the signal on atleast two sensors, and the method further comprises: oversampling thereceived signal.
 10. The process according to claim 9, wherein asampling period corresponds to T/p.